PRP Records

Probable Primes Top 10000

(293016 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9001(50891^20431-1)/5089096157Serge Batalov06/2022
9002(50^56597+1)/5196155Robert Price03/2014
900322313^20374+20374^2231396149Hans Havermann12/2019
900422279^20668+20668^2227996141Hans Havermann11/2019
9005(41*10^96137-59)/996138Robert Price10/2017
90062^319353-11034396135Enzo Doria05/2014
900711^92309-4296130Lelio R Paula05/2016
9008(21675^22171-1)/2167496129Serge Batalov06/2022
900914^83869-13^8386996125Jean-Louis Charton01/2009
9010(7*10^96112+143)/396113Robert Price04/2016
901126731^3940+3940^2673196112Hans Havermann07/2020
901222640^17583+17583^2264096109Hans Havermann07/2020
9013(19178^22441-1)/1917796107Serge Batalov06/2022
90142^319237+6583596100Lelio R Paula03/2016
90152^319194-184196087Yves Minet03/2013
901623949^10280+10280^2394996084Hans Havermann07/2020
9017(1927^29251-1)/192696083Serge Batalov06/2022
901820^73847-3196078Lelio R Paula05/2016
9019(60229^20101-1)/6022896075Serge Batalov06/2022
9020(28044^21601-1)/2804396074Serge Batalov06/2022
902150^56543-4996065Norbert Schneider09/2018
90222^319107-10955596061Enzo Doria04/2014
9023(3*2^319114-1)/262796060Lelio R Paula02/2014
90242^319098-11215796059Enzo Doria06/2014
902515^81673+9496055Lelio R Paula07/2016
9026(85761^19471-1)/8576096052Serge Batalov06/2022
90272^319074+187174996051Enzo Doria05/2016
902825670^5517+5517^2567096050Hans Havermann06/2020
90296*10^96037+1996038Robert Price11/2021
90302^319007-11211196031Enzo Doria06/2014
9031(57987^20161-1)/5798696029Serge Batalov06/2022
90332^318946-142196013Yves Minet01/2013
9032(68310^19861-1)/6830996013Serge Batalov06/2022
9034(20294^22291-1)/2029396012Serge Batalov06/2022
9035(304^38669-1)/30396008Serge Batalov06/2022
9036(1840^29401-1)/183995986Serge Batalov06/2022
903722830^16003+16003^2283095982Hans Havermann02/2020
90382^318834-11041195979Enzo Doria05/2014
90392^318831-196595978Lelio R Paula03/2016
9040(5*10^95976+7)/395977Erik Branger03/2014
9041(12797^23369-1)/1279695975Serge Batalov06/2022
9042(10534^23857-1)/1053395963Serge Batalov06/2022
904322871^15696+15696^2287195962Hans Havermann01/2020
9044(2^318760+858)/295957Stefano Morozzi02/2021
904523167^13860+13860^2316795953Hans Havermann01/2020
9046(823^32911-1)/82295946Serge Batalov06/2022
90485*3^201089-895945Lelio R Paula08/2014
9047(81783^19531-1)/8178295945Serge Batalov06/2022
90492^318711-13995942Lelio R Paula11/2012
90502^318635-116795919Lelio R Paula03/2016
905115^81555+1695917Lelio R Paula07/2016
9052(37*10^95895+377)/995896Robert Price10/2017
9053(22699*2^318527+1)/2195890Lelio R Paula07/2014
90542^318496-9730595877Lelio R Paula03/2016
905522129^21496+21496^2212995871Hans Havermann07/2020
90572^318466+1501595868Lelio R Paula03/2016
905624847^7216+7216^2484795868Hans Havermann07/2020
905823706^11065+11065^2370695866Hans Havermann07/2020
9059(2863^27733-1)/286295865Serge Batalov06/2022
90606^123187-17312995859Mike Oakes04/2011
90612^318423-48795855Yves Minet03/2012
906210^95848+44370995849Patrick De Geest10/2022
906310^95848-500000000195848Robert Price09/2022
906410^95848-6197195848Patrick De Geest10/2022
9065(2^318359+678)/295836Stefano Morozzi09/2020
9066(10223*2^318350+1)/156395834Lelio R Paula07/2014
9067(8060^24533-1)/805995831Serge Batalov06/2022
9068(9853^23993-1)/985295814Serge Batalov06/2022
9070(2^318267+2550)/295808Stefano Morozzi09/2020
9069(5048^25873-1)/504795808Serge Batalov06/2022
90724*10^95799+1395800Robert Price02/2021
9071(65533^19891-1)/6553295800Serge Batalov06/2022
907345369!2+102495787Robert Price02/2015
90743^200758-8695786Lelio R Paula05/2016
9075(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
9076(2^318171+2030)/295779Stefano Morozzi09/2020
90773*10^95776-5995777Robert Price10/2017
9078(82970^19471-1)/8296995772Serge Batalov06/2022
9079193^41901-295768Lelio R Paula10/2017
9080(2^318124+2502)/295765Stefano Morozzi09/2020
9081(12900^23297-1)/1289995761Serge Batalov06/2022
90824*10^95752-7195753Robert Price11/2017
9083(16955^22639-1)/1695495743Serge Batalov06/2022
9084(81795^19489-1)/8179495740Serge Batalov06/2022
9085(2742^27847-1)/274195737Serge Batalov06/2022
9086(6072^25303-1)/607195726Serge Batalov06/2022
908723640^11197+11197^2364095721Hans Havermann12/2019
908810^95712+8932995713Patrick De Geest09/2022
909010^95712-400000195712Robert Price07/2021
908910^95712-98931395712Patrick De Geest09/2022
9091(60657^20011-1)/6065695706Serge Batalov06/2022
9092((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
9093(509203*2^317881-1)/5280595693Lelio R Paula04/2015
9094(26161^21661-1)/2616095687Serge Batalov06/2022
9095(2^317853+1086)/295683Stefano Morozzi09/2020
90964*10^95672+9195673Robert Price11/2017
90976*10^95665+4395666Robert Price07/2020
9098(20819^22153-1)/2081895663Serge Batalov06/2022
9099(64464^19891-1)/6446395658Serge Batalov06/2022
9100(934^32203-1)/93395652Serge Batalov06/2022
9101(11*10^95641-113)/395642Robert Price01/2017
9102(72330^19681-1)/7232995632Serge Batalov06/2022
9103(13224^23203-1)/1322395624Serge Batalov06/2022
9104(18211^22441-1)/1821095602Serge Batalov06/2022
9105(71975^19681-1)/7197495590Serge Batalov06/2022
9106(13*10^95588+11)/395589Robert Price05/2015
9107Phi(191188,10)/19118995587Maksym Voznyy11/2015
9108(13368^23167-1)/1336795585Serge Batalov06/2022
9109(25874^21661-1)/2587395583Serge Batalov06/2022
91103^200325+7095580Lelio R Paula05/2016
9111(25*10^95574-7)/995575Robert Price12/2014
9112(2^317485-3)/2131395569Lelio R Paula06/2013
91132^317464+3195567Lelio R Paula11/2012
9114(2^317451+2114)/295562Stefano Morozzi09/2020
91157^113073+8295558Lelio R Paula04/2016
9116(24728^21751-1)/2472795552Serge Batalov06/2022
9117(49764^20341-1)/4976395536Serge Batalov06/2022
9118(36155^20959-1)/3615495531Serge Batalov06/2022
9119(7725^24571-1)/772495526Serge Batalov06/2022
9120(20546^22147-1)/2054595510Serge Batalov06/2022
91212^317251+46595503Lelio R Paula03/2016
912219^74684+5895503Lelio R Paula06/2016
9123(2^317250-7)/33995500Lelio R Paula07/2013
91245*10^95498-2195499Robert Price12/2021
9125(21615^22031-1)/2161495495Serge Batalov06/2022
91266^122718-7995494Lelio R Paula05/2016
912722168^20291+20291^2216895485Hans Havermann10/2019
9128(77427^19531-1)/7742695481Serge Batalov06/2022
9129(13026^23203-1)/1302595472Serge Batalov06/2022
91302^317141-11049195469Enzo Doria05/2014
9131(2^317097+3014)/295456Stefano Morozzi09/2020
91322^317094+7630995455Enzo Doria05/2016
91332^317085+9595453Lelio R Paula11/2012
9134(17*10^95451-377)/995452Robert Price11/2017
91352^317057-10955195444Enzo Doria04/2014
91363^200026+2895437Lelio R Paula05/2016
91372^317024+9395434Donovan Johnson06/2008
9138(86*10^95428-437)/995429Robert Price03/2021
913910^95427+19259195428Patrick De Geest05/2021
91422^316999+160595427Lelio R Paula03/2016
9141(2^317000+3210)/295427Stefano Morozzi09/2020
914010^95427-1000195427Robert Price02/2021
91432^316995-11042795426Enzo Doria05/2014
9144(69841^19699-1)/6984095420Serge Batalov06/2022
9145(59242^19993-1)/5924195415Serge Batalov06/2022
914722300^18987+18987^2230095410Hans Havermann06/2020
9146(9478^23993-1)/947795410Serge Batalov06/2022
91482^316937+17795408Lelio R Paula11/2012
91494*10^95407+9195408Robert Price11/2017
91502^316908+191595399Lelio R Paula03/2016
91512^316894+9995395Lelio R Paula11/2012
9152(2^316887+2546)/295393Stefano Morozzi09/2020
91532*10^95374-2195375Robert Price09/2020
91546^122547+1195361Lelio R Paula05/2016
91552^316771+8287595358Lelio R Paula03/2016
9156(15609^22741-1)/1560895358Serge Batalov06/2022
9157(2^316765+3102)/295356Stefano Morozzi09/2020
9158(2267^28411-1)/226695329Serge Batalov06/2022
9159(824^32693-1)/82395328Serge Batalov06/2022
9160(23*10^95326+1)/395327Serge Batalov05/2009
91611*10^95326+5795327Robert Price03/2011
916210^95326-39368795326Patrick De Geest09/2013
9163(3^199803+4)/47953995325Lelio R Paula04/2013
91642^316654-10948195323Enzo Doria04/2014
91658*10^95316+5195317Robert Price05/2017
9166(50^56099+43^56099)/9395309Serge Batalov12/2016
9167(23*2^316559+1)/392595292Lelio R Paula09/2013
9169(71*10^95277-539)/995278Robert Price11/2017
916823422^11691+11691^2342295278Hans Havermann10/2019
917019^74503-5695271Lelio R Paula06/2016
9171(5038^25733-1)/503795267Serge Batalov06/2022
917211^91475-438095262Enzo Doria01/2013
9173(62*10^95251-611)/995252Robert Price05/2017
9174(160090^18301-1)/16008995240Serge Batalov06/2022
9175(173205^18181-1)/17320495238Serge Batalov06/2022
9176(158710^18313-1)/15870995234Serge Batalov06/2022
9177(9979^23813-1)/997895227Serge Batalov06/2022
9178(57376^20011-1)/5737595223Serge Batalov06/2022
9179(2^316321-509203)/6937795218Lelio R Paula06/2013
918026541^3868+3868^2654195216Hans Havermann07/2020
9181(79*10^95214-43)/995215Erik Branger11/2013
9182(7176^24691-1)/717595202Anonymous11/2020
9183(9*2^316233-1)/175195194Lelio R Paula02/2014
91845*2^316213+995191Lelio R Paula08/2014
91852*10^95188-9195189Robert Price04/2020
91862^316205-184816395188Enzo Doria07/2015
91872^316185-278791395182Enzo Doria04/2016
9188(2^316174+3538)/295178Stefano Morozzi09/2020
9189(9787*2^316142-1)/395172Lelio R Paula04/2015
91902^316140-595168Henri Lifchitz02/2006
9191(15185*2^316117-1)/395165Lelio R Paula04/2015
9192(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
91932^316069+7681795147Enzo Doria05/2016
9194(199*10^95134-7)/395136Robert Price02/2017
91952^316027-9730595134Lelio R Paula03/2016
91962^316006-279805195128Enzo Doria04/2016
919724994^6397+6397^2499495127Hans Havermann02/2020
91992^315921-279760395102Enzo Doria04/2016
9198(2^315921+1314)/295102Stefano Morozzi02/2021
92002*10^95095+6395096Robert Price10/2017
92012^315857+129995083Lelio R Paula03/2016
9202(2^315858+2598)/295083Stefano Morozzi09/2020
920414^82955-4395078Lelio R Paula06/2016
9203(8*10^95078-269)/995078Robert Price09/2021
9205(23*10^95074-101)/395075Robert Price04/2021
92062^315827-93307595074Paul Bourdelais04/2021
9207(2*10^95072-17)/395072Robert Price08/2014
9208(286*10^95059-1)/395061Robert Price11/2020
9209(2^315779+1610)/295059Stefano Morozzi09/2020
92102^315775-11154643595058Paul Bourdelais10/2021
921121938^21513+21513^2193895051Hans Havermann09/2020
92122^315727+6595044Lelio R Paula11/2012
92132^315725+188575795043Enzo Doria03/2017
921423277^12058+12058^2327795000Hans Havermann09/2020
92151*10^94983+2194984Robert Price03/2011
921610^94983-71794983Patrick De Geest08/2013
921717^77187-8294975Lelio R Paula07/2016
92183*10^94964+3794965Robert Price10/2017
9219(2^315481-1017)/2062728594962Lelio R Paula06/2013
92202^315423-11032994952Enzo Doria05/2014
922111^91169-723094943Enzo Doria02/2013
92227*10^94938+6194939Robert Price02/2017
92232^315351+102594931Lelio R Paula03/2016
92242^315350-11225394930Enzo Doria06/2014
9225(2^315343+1766)/294928Stefano Morozzi09/2020
9226(2^315343+3066)/294928Stefano Morozzi09/2020
9229((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
92282^315268+794906Lelio R Paula10/2012
922711^91133+6294906Lelio R Paula05/2016
9230(2^315264+1558)/294904Stefano Morozzi09/2020
923130^64244+4194897Lelio R Paula08/2012
9232(151*10^94885-7)/994887Robert Price07/2017
92334^157583+2214794875Mike Oakes01/2011
9234(14*32^63026-190819)/3194864Eric Chen04/2023
92352^315098+12394854Lelio R Paula11/2012
92363^198791-3494848Robert Price11/2013
92373*2^315067+794846Lelio R Paula08/2014
9238(9*2^315057+1)/7394841Lelio R Paula09/2013
923922576^15875+15875^2257694836Hans Havermann09/2020
9240(16*10^94822+53)/394823Robert Price12/2016
92418*6^121849-794818Lelio R Paula10/2014
9242(85*10^94802+473)/994803Robert Price03/2017
924321767^21852-21852^2176794790Norbert Schneider06/2020
9244(2*34^61893-647)/394788Eric Chen03/2023
92452^314870-10876194786Enzo Doria03/2014
92465*2^314841-394778Lelio R Paula08/2014
9248(2^314842+550)/294777Stefano Morozzi09/2020
924711738^23289-23289^1173894777Norbert Schneider05/2022
9249(2^314787+2630)/294761Stefano Morozzi09/2020
92506^121772+11394758Lelio R Paula05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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